Giza's older districts contain a number of significant Ottoman and Mamluk mosques that receive a fraction of the attention of the pharaonic monuments but are genuinely worth visiting. Most are open to non-Muslim visitors outside of prayer times, and Egyptian mosques are generally welcoming to respectfully dressed foreign visitors who take off their shoes at the entrance.
The mosques in the residential areas west and south of Giza station tend to be quieter and more atmospheric than the tourist-circuit sites. Ask at your hotel about the nearest historic mosque; most staff will point you in a useful direction. Visiting a working Egyptian mosque — where people genuinely come to pray, chat with friends, and sleep in the cool shade of the afternoon — gives a completely different view of the city from the museum and monument circuit. Modest clothing (covered arms and legs; women a headscarf) is expected.